Generally the term "organic" in terms of mental illness implies that the problem is physiological in origin, that is, there's something physically "wrong" - some neurons firing drastically wrongly or some malformation in the brain perhaps.
This means that your mental illness is not simply a psychological issue, and consequently it won't get better without some kind of physical intervention (usually).
The good news is that, for the vast majority of people, DP/DR is not organic in origin - and if it is, it hardly ever on its own is evidence for a serious physiological problem.